.172 
NATURE 
[APRIL 25, 1999 

This certainly requires more explanation than is 
given. The words “of course no terms must be 
omitted”? begs the whole question; the sum is 
a limit, and we cannot take all the terms. Perhaps 
5) 
be 
‘ 
Let Sum 
1 
convergent as it stands, so that Lt(7—x )um=0. 
the following might be suggested. 
S 
Let Sv, be so related to Sz, that there is a one-one 
1 
correspondence of terms, so that we can write 
Uum=Um, Un=*n, 
where m’, n’ are determined by m, n respectively. 
Suppose further that when m—o, then m’—wx, 
and that when then 7’-+0o; in these 
circumstances we can infer that Sv,»=Svp. So 
far as Mr. Hardy’s proof goes, we might infer 
that— 
U, +s +u, t+ oe oO 
N—O , ee) 
=U tate it gto ato = 
but this is not true, unless u, occurs at a finite 
place on the right. 
(3) The contents of the last volume of the 
London Mathematical Society’s proceedings are, 
as usual, very varied, and only a very gifted or 
very conceited reviewer would venture to express 
an opinion on the absolute or relative value of the 
different papers. As specimens, we note Mr. 
Bromwich’s on Foucault’s pendulum, Mr. Burn- 
side’s on prime-power groups, Mr. Carslaw’s on 
Green’s function for A?u+k2u=0, Mr. Hobson’s 
on the linear integral equation, and Sir J. Lar- 
mor’s on the electromagnetic force on a moving 
charge. There is also an interesting paper by 
Mr. Mordell on the diophantine equation 
y?—k=x*. Altogether, the volume gives an 
encouraging view of the state of English mathe- 
matics, except for the lack of geometry, especially 
pure geometry. This is becoming really a serious 
symptom; not only is there an element of culture 
in geometry which analysis does not possess, but 
there is a risk of our studying the whole science 
from a one-sided point of view, even if (as is 
probable) strict mathematical geometry is reduced 
to formal logic applied to a few indefinable 
axioms. G. B. M. 
PSYCHOLOGY AND PHILOSOPHY. 
(1) The Foundations of Character, Being a Study 
of the Tendencies of the Emotions and Senti- 
ments. By A. F. Shand. Pp. xxxi+ 532. 
(London: Macmillan and Co., Ltd., 1914) 
Price 12s. net. 
(2) Perception, Physics, and Reality: An Enquiry 
into the Information that Physical Science can 
Supply about the Real. By C. D. Broad. Pp. 
xli+ 388. (Cambridge: At the University Press, 
1914.) Price ios. net. 
NO. 2372, VOL. 95| 
: (3) Philosophy: What is it? By Prof. F. B. 
Jevons. Pp. vii+135. (Cambridge: At the 
University Press, 1914.) Price 1s. 6d. net. 
(4) Know Your Own Mind. A Little Book of 
Practical Psychology. By W. Glover. Pp. 
ix+204. (Cambridge: At the University Press, 
1914.) Price 2s. net. ‘ 
(1) SYCHOLOGISTS have been slow to 
meet the popular demand for a science 
of character. Under the name ethology, it was 
planned by John Stuart Mill. But Mill failed to 
accomplish his plan. The ‘laws of psychology,’ 
upon which he proposed to base his new science, 
were, in his day, inadequate and unsuitable for 
the task. In Mr. Shand’s eagerly awaited book 
the attempt has been renewed. Will the new 
attempt meet with a greater success? 
Judged by Mr. Shand’s criterion, it undoubtedly 
will. Mr. Shand no longer claims to deduce the 
laws of character from certain fundamental con- 
ceptions, initially established as true. He seeks 
rather to formulate provisional hypotheses, and 
to test them by their fruitfulness. His method is 
thus concrete and synthetic. It gives him the 
viewpoint of the novelist and dramatist, of the 
biographer and historian; and enables him to 
utilise their material. In place of Mill’s ‘laws of 
association ’ he propounds the * principle of organ- 
isation ’: all mental activity tends to produce and 
sustain system; and, in sharp distinction from the 
school of Mill, and in common with others who 
have more recently approached his field, he seeks 
the springs of conduct on the instinctive and 
emotional side of man’s original nature, rather 
than on its intellectual side. 
In his conception of character the chief place 
is given to those lower systems called emotions, 
and those higher systems, which he has already 
taught us to call ‘sentiments.’ The influence of 
intelligence and will is somewhat briefly dismissed. 
He treats more fully the influence of tempera- 
ment; and, most suggestively, that of temper. 
The present volume deals in detail with each of 
the primary emotions. Together with fear, anger, 
wonder, and disgust, he «includes repugnance, 
surprise, sorrow, and joy. Tenderness, self- 
assertion, and self-submission are omitted. His 
list thus differs a little from that suggested 
by Mr. McDougall. A yet deeper differ- 
ence is revealed in his treatment of instinct. 
In Mr. McDougall’s view, to each principal 
instinct there corresponds innately some one 
specific emotion. According to Mr. Shand, an 
emotion may include within its system several 
instincts, and the same instinct may be found 
organised in several different emotions. The 
: difference is partly a question of fact, which future 

